Pumphrey scored on a 13-yard first-quarter run and on a 38-yard TD catch early in second that gave the Aztecs (4-3, 3-0 Mountain West Conference) a 14-0 lead. He finished with 20 runs for 152 yards and three catches for 55 yards.
San Jose State (3-4, 2-2) scored its only points on Kenny Potter's 1-yard keeper to make it 14-7 with 4:27 left in the first half.
Donny Hageman kicked three field goals and Chase Price scored on a 1-yard TD run for San Diego State to end the game with 16 straight points.
The Aztecs host Utah State on Friday night. The Aggies beat No. 21 Boise State 52-26 on Friday night and are the only other Mountain West team with an undefeated conference record.